To find the dollar amount of fees paid for investing $$61,500$ in the Yamaha Aggressive Growth Fund with an expense ratio of $1\mathrm{.}84$ percent, we can use the following calculation:

Fees $=$ Investment Amount $*$ Expense Ratio

Fees $=$ $$61,500*1\mathrm{.}84\%$

First, let's convert the percentage to a decimal:

Expense Ratio $=1\mathrm{.}84\%=1\mathrm{.}84/100=0\mathrm{.}0184$

Now, calculate the fees:

Fees $=$ $$61,500*0\mathrm{.}0184$

$$ $$1,132\mathrm{.}40$

So$,$ if you invest $$61,500$ in the Yamaha Aggressive Growth Fund, you would pay approximately $$1,132\mathrm{.}40$ in fees for the year.